Compute the GRPO advantages when every rollout in the group scores 1.0

**All four advantages are 0**, and the group contributes no policy-gradient signal. GRPO (Group Relative Policy Optimization) normalizes each sample's reward relative to its group's mean and standard deviation: $$A_i = \frac{r_i - \bar{r}_{\text{group}}}{\sigma_{\text{group}} + \epsilon}$$ With rewards `[1.0, 1.0, 1.0, 1.0]`, the group mean is also 1.0. Every numerator becomes `1.0 - 1.0 = 0`, and dividing zero by anything is still zero. The epsilon in the denominator only protects against division by zero when std is small; it cannot create signal where none exists. GRPO has no value network. The group itself is the baseline. The signal it produces is purely the contrast between rollouts (sampled answers) on the same prompt. When the contrast vanishes (all-pass or all-fail), the prompt cannot teach the policy anything in that update. The operational fix is to detect saturated groups before they hit the gradient step. Filter all-pass and all-fail groups out, raise prompt difficulty as the model improves, or mix harder examples into the data pool so groups keep containing both successes and failures.

**Advantages are [0, 0, 0, 0]; the group contributes zero policy-gradient signal.** GRPO replaces the PPO value network with a per group baseline computed directly from the rollouts: $$A_i = \frac{r_i - \bar{r}_{\text{group}}}{\sigma_{\text{group}} + \epsilon}$$ For `[1.0, 1.0, 1.0, 1.0]`, the mean is 1.0 and the standard deviation is 0. Every numerator is 0, so the normalization does not matter. The epsilon prevents NaN from a zero denominator; it does not create a learning signal. This is a structural property of GRPO, not a bug. The algorithm trades the value network (which can assign a non-zero advantage to a 1.0 reward in absolute terms) for the cheaper group baseline. The cost is that any prompt where every rollout collapses to the same reward produces zero gradient. In RLVR training (verifiable rewards: math checkers, unit-test runners), this happens routinely. Easy prompts the model has mastered produce all-pass groups; hard prompts beyond the model's reach produce all-fail groups. Both contribute zero. **Operational mitigations** used in practice: filter saturated groups before computing gradients, and schedule curriculum so prompt difficulty rises with the model's pass rate. Sample mixed-difficulty data so most groups carry contrast, and track the fraction of saturated groups as a training health metric.